Molinari holed a 5-foot birdie putt at No. 18 to take the outright lead, leaving Xander Schauffele alone in second place on 7 under.
Both now sit at five under par heading into the final Sunday, with a four-shot gap between them and the leaders Jordan Speith, Kevin Kisner and Xander Schauffele.
Molinari became Italy's first Champion Golfer by carding a flawless two-under-par round to get in at -8 on a day that saw Tiger Woods, Jordan Spieth and Rory McIlroy all challenge as the lead chopped and changed.
The 14-time major victor was briefly the outright lead at Carnoustie on an absorbing final day as he makes an improbable bid to win his first major title since 2008.
Molinari's victory ended an American stranglehold on golf's major championships, with a USA golfer having won the previous five.
After a double-bogey on the 17th hole on Friday, Molinari didn't drop another shot on his last 37 holes of the tournament.More news: Merck lowers prices of medications including hepatitis C drug
It could also lead to early players leapfrogging over the group of players - and there are seven in all - tied with Woods for sixth place and making it even more hard to move up the leaderboard.
Playing in his traditional last-day red shirt, Woods continued to turn the screws.
Eddie Pepperell says he was a "little hung over" during his round of 4-under 67 that has left him one shot off the lead at the British Open.
He played the opening nine holes in 34 strokes, sinking birdies at the fourth and sixth. Instead of trying to route his shot around the gallery at Carnoustie, he decided, hell with it, I'm going right at 'em. He managed to punch down the fairway then hit a 60-degree wedge from 83 yards to a few feet to save par.
And Woods' playing partner sensed an aura around the 14-time major champion.
Rory finished tied second after a rollercoaster of a final round.More news: Here’s How to Sign Up for the PlayStation 4 6.0 Beta
The American could get the battle with Tiger Woods he has always visioned with the 14-time major victor lurking ominously among the chasing pack after a thrilling day of low scoring at a defenceless Carnoustie.
Tiger Woods appeared ready to end his 10-year victory drought in majors midway through the round.
Only three of the first 42 players to complete their rounds on Sunday scored in the 60s.
McIlroy and Justin Rose, with five majors and an Olympic gold between them, both eagled the 14th to eventually post the clubhouse lead.
Further trouble and another dropped shot was to follow at the next and it was with his head bowed deep in thought he strode down the par-three 13th where he managed to stem the haemorrhage with a par.
Woods was four shots behind.More news: Vintage Tiger Woods boosts Open hopes with terrific round
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